I am a theoretical physicist working on the effects of topology and geometry in condensed matter physics. In particular, I am interested in packing problems, foams and the role played by conformal geometries in these systems.
Phyllotaxis, disk packing and Fibonacci numbers
A. Mughal and D. Weaire arXiv:1608.05824 (2016).
We consider the evolution of the packing of disks (representing the position of buds) that are introduced at the top of a surface which has the form of a growing stem. They migrate downwards, while conforming to three principles, applied locally: dense packing, homogeneity and continuity. We show that spiral structures characterised by the widely observed Fibonacci sequence (1,1,2,3,5,8,13...), as well as related structures, occur naturally under such rules. Typical results are presented in a animation.
Projection of cylindrical disk packings on to a stem
An experimental study of columnar crystals using monodisperse microbubbles.
A. J. Meagher, F. Garcıa-Moreno, J. Banharta, A. Mughal and S. Hutzler. Colloids and Surfaces A (2015).
We investigate the ordered arrangements of monodisperse microbub- bles confined within narrow cylinders. These foams were imaged using X-ray tomography, allowing the 3D positions of the bubbles of the foam to be accurately determined. The structure of these foams closely re- semble the minimum energy configuration of hard spheres in cylindrical confinement as found in simulations. For larger ratios, λ, of cylinder to bubble diameter two- and three-layered crystals were formed. Each layer of these structures is found to be ordered, with each internal layer resem- bling structures found at lower λ values. The average number of contacts per bubble is seen to increase with λ.
Columnar crystals using monodisperse microbubbles
Theory of cylindrical dense packings of disks. A. Mughal & D. Weaire. Physical Review E (2014)
We have previously explored cylindrical packings of disks and their relation to sphere packings. Here we extend the analytical treatment of disk packings, analysing the rules for phyllotactic indices of related structures and the variation of the density for line-slip structures, close to the symmetric ones. We show that rhombic structures, which are of a lower density, are always unstable i.e. can be increased in density by small perturbations
Theory of cylindrical dense packing of disks